Hilbert basis theorem for generalized Noetherian rings
UDC 512.552 We explore the Hilbert Basis Theorem for uniformly $S$-Noetherian rings, $S$-$w$-Noetherian rings, and uniformly $S$-$w$-Noetherian rings. Moreover, we also show that uniformly $S$-($w$-)Noetherian rings may be not ($w$-)Noetherian even in the case where $S$ consists of nonzero divisors.
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| Datum: | 2026 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9329 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 512.552
We explore the Hilbert Basis Theorem for uniformly $S$-Noetherian rings, $S$-$w$-Noetherian rings, and uniformly $S$-$w$-Noetherian rings. Moreover, we also show that uniformly $S$-($w$-)Noetherian rings may be not ($w$-)Noetherian even in the case where $S$ consists of nonzero divisors. |
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| DOI: | 10.3842/umzh.v78i5-6.9329 |